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3-space absolutely convergent An+1 apply boundary bounded set choose closed curve compute coordinate Corollary corresponding defined definition derivative differential forms divergent domain dudv dxdy dxdydz dydz dzdx equation equivalent evaluate example Exercise exists f is continuous f(po f(xo formula function f given graph Green's theorem improper integral integrand interval inverse Jacobian Let f Let f(x lim f(x line segment linear transformation mapping matrix mean value theorem neighborhood notion obtain one-to-one open set orientation p₁ plane polynomial proof prove R(Ap real numbers rectangle region region D sequence set of points Show surface T(po uniformly continuous uniformly convergent variables vector write zero ди ди дх მა მე მყ